Convergence to separate variables solutions for a degenerate parabolic equation with gradient source

Details Convergence to separate variables solutions for a degenerate parabolic equation with gradient source Convergence to separate variables solutions for a degenerate parabolic equation with gradient source

2010-05-20

arxiv.org/abs/1005.3606v1

Journal of Dynamics and Differential Equations 24 (2012) 29-49

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s10884-011-9238-x

The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is shown for global solutions. The proof relies on the half-relaxed limits technique within the theory of viscosity solutions and on the construction of suitable supersolutions and barrier functions to obtain optimal temporal decay rates and boundary estimates. Blowup of weak solutions is also studied.

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